How to add linked groups symmetrically around an object
I would suggest Array modifier. You need to turn off the two checkboxes for constant and relative displacement, and place an empty on top of the object you want to duplicate. Then, you change the center of rotation to the 3D cursor, then set the empty as the object in the Array modifier, and move the 3D cursor to the center of your model. Increase the number of array iterations by however many objects you want on the outside, then divide 360 by the number of iterations to find out how much you need to rotate the empty. It's a slightly convoluted way of using the array modifier, but it works for me. 

Sometimes there will be a freaky scaling problem when you turn on the array modifier, but it can be fixed by pressing ctrl A --> apply scale.